equilibrium with a third are in thermal equilibrium with each other. First low:

When equal quantities of niechanical effect are produced by any means whatever from purely thermal effects, equal quantities of heat are put out of

existence or are created. S'ccoizd lnzw: It is impossible to transfer heat from

a cold body to a hot body without the perfornlance of mechanical work. Third

lnzv: I t is impossible by any means whatever to superpose only the images of

several light sources to obtain an image brighter than the brightest of the

source.

7

Aldrich et al., Science, vol. 106, p. 225, 1947.

SMITHSONIAN PHYSICAL TABLES

10

Part 3.-Electric

and Magnetic Units

A system of units of electric and magnetic quantities requires four fundamental quantities. A system in which length, mass, and time constitute three

of the fundamental quantities is known as an “absolute” system. There are

two abso1u:e systems of electric and magnetic units. One is called the electrostatic, in which the fourth fundamental quantity is the dielectric constant, and

one is called the electromagnetic, in which the fourth fundamental quantity is

magnetic permeability. Besides these two systems there will be described a

third, to be known as the absolute system, that was introduced January 1, 1948.

(See Table 4.)

I n the electrostatic system, unit quantity of electricity, Q, is the quantity

which exerts unit mechanical force upon an equal quantity a unit distance from

it in a vacuum. From this definition the dimensions and the units of all the

other electric and magnetic quantities follow through the equations of the

mathematical theory of electromagnetism. The mechanical force between two

quantities of electricity in any medium is

Q Q’

F= -

KrZ ’

where K is the dielectric constant, characteristic of the medium, and r the distance between the two points at which the quantities Q and Q‘ are located. K

is the fourth quantity entering into dimensional expressions in the electrostatic

system. Since the dimensional formula for force is [ M L T 2 ] ,that for Q is

[M’LZ T ’ K ’ ] .

The electroinagnetic system is based upon the unit of the magnetic pole

strength (see Table 466). The dimensions and the units of the other quantities

are built up from this in the same manner as for the electrostatic system. The

mechanical force between two magnetic poles in any medium is

m d

F= pr2 ’

in which p is the permeability of the medium and Y is the distance between two

poles having the strengths m and m‘. p is the fourth quantity entering into

dimensional expressions in the electromagnetic system. I t follows that the

dimensional expression for magnetic pole strength is [M’L:T 1 p * ] .

The symbols K and p are sometimes omitted in tlie dimensional formulae so

that only three fundamental quantities appear. There are a number of objections to this. Such formulae give no information as to the relative magnitudes

of the units i n the two systems. The omission is equivalent to assuming some

relation between mechanical and electrical quantities, or to a nlechanical explanation of electricity. Such a relation or explanation is not known.

The properties I< and p are connected by the equation I / V / K p = v , where v

is the velocity of an electromagnetic wave. For empty space or for air, K and

p being measnred in tlie same units, 1VKp=c, where c is the velocity of

light in vacuo, 2 . 9 9 7 7 6 ~10’O cni per sec. It is sometimes forgotten that the

omission of the dimensions of K or p is merely conventional. For instance,

magnetic field intensity and magnetic induction apparently have the same dimensions when p is omitted. This results in confusion and difficulty in understantling the theory of magnetism. The suppression of p has also led to the use

of the “centimeter” as a unit of capacity and of inductance ; neither is physically

the same as length.

SMITHSONIAN PHYSICAL TABLES

11

ELECTROSTATIC SYSTEM

Capacitance of an insulated conductor is proportional to the ratio of the

quantity of electricity in a charge to the potential of the charge. The dimensional formula is the ratio of the two formulae for electric quantity and

potential or [M'L:T-lK'/M'L'T-'K-'] or [ L K ] .

Conductance of any part of an electric circuit, not containing a source of

electromotive force, is the ratio of the current flowing through it to the difference of potential between its ends. The dimensional formula is the ratio of the

formulae for current and potential or [M'L;T-2K'/M'L'T'K-i] or [ L T - l K ] .

Electrical conductivity, like the corresponding term for heat, is quantity

per unit area per unit potential gradient per unit of time. The dimensional

formula is [ M ' L g T ' K 4 / L 2 ( M 4 L

*TT-'Ki

/ L ) T ] or [ T ' K ] .

Electric current (statampere-unit quantity) is quantity of electricity flowinn through a cross section per unit of time. The dimensional formula is the

raTio of tKe formulae for electric quantity and for time or [ M * L > P K ' / T or

]

[M3L;T2K'],

Electric field intensity strength at a point is the ratio of the force on a

quantity of electricity at a point to the quantity of electricity. The dimensional

formula is therefore the ratio of the formulae for force and electric quantity or

[ M L T-2/M L 2 T-lK' ] or [ h14L-3 T-lK-' I .

Electric potential difference and electromotive force (emf) (statvoltwork = 1 erg) .-Change of potential is proportional to the work done per unit

of electricity in producing the change. The dimensional formula is the ratio of

the formulae for work and electrical quantity or [ML2Z'2/M'L;T1K4]or

[MiLiT-'K-'].

Electric surface density of an electrical distribution at any point on a surface is the quantity of electricity per unit area. The dimensional formula is the

ratio of the formulae for quantity of electricity and for area or [ M'L-' T ' K ' ] .